Re: [EM] RE : Re: RE : Majority Criterion, hidden contradictions

[Chris Benham]

Abd ul-Rahman Lomax wrote: No, Range does this. If we assume that voters express their expected value for the various candidates, the expected value for the voters, collectively, is the sum of the individual expectations. Sure, but I don't see how this assumption can be taken for granted. No election method can extract information from the voters and use it to determine the winner if the voters do not express the information. The assumption cannot be taken for granted, which is exactly why I expressed it as an assumption. However, what is being said is that if people use Range sincerely and honestly, Range will maximize expected value, summed over all the voters. Yes, but how many of  "the people"? 90: A9>B1    (sincere is A9>B1) 10: B99>A0  (sincere is B5>A3) All the voters have a sincere low opinion of both candidates, but 90% think that A is 900% better than B and yet B wins (with only 10% of the voters not being "sincere and honest"). Consider a diagnostic tool, a questionnaire to be filled out to determine health status and medical treatment. If people lie on the questionnaire, the results will be suboptimum. Now, the question then becomes, will people lie? Some will, depends on the definition of "lie." The definition is fuzzy because the voters are not even being asked a clear unambiguous question. Here is the paradox: if voters care little about whether or not A or B wins, but want A to win, they can distort the rating of B. For the condition to be true, the voters must simultaneously "care little" and care enough to lie about their true preferences. That rests on the false assumption that it is (significantly) more bother to lie than to tell the truth. In fact it seems to me to be less bother. I can well imagine being sure that I prefer A to B but not sure exactly what my honest rating of each is, so I'd find it easier to vote A max. and B min. My real point is that we don't know, very well, how voters will actually behave. We very much need real-world examples, theory will only take us so far. If we can't make this assumption then there is no guarantee that Range will outperform a majoritarian method in terms of expected value. We can certainly be sure majoritarian methods will outperform  Range in the worst-case scenarios. Chris Benham

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